Indefinite Integrals Polynomial, Trig, Logs and Exp

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Indefinite integrals are integrals in the form of
intf(z)dz,
intf(z)dz,

There is no lower or upper bound and it is not defined in a region.

- Properties of Indefinite Integrals

o ∫kf(x)dx = k∫f(x)dx for any constant k

o ∫(f(x) ± g(x))dx = ∫f(x)dx ± ∫g(x)dx

- Power Formulas

o ∫undu = [(un+1)/(n+1)] + C ∫u-1du = ∫(1/u)du = lnu + C

- Trigonometric Formulas

o ∫(cosu)du = sinu + C ∫(sinu)du = -cosu + C

o ∫(sec²u)du = tanu + C ∫(csc²u)du = -cotu + C

o ∫(secutanu)du = secu + C ∫(cscucotu)du = -cscu + C

- Exponential and Logarithmic Formulas

o ∫(eu)du = (eu) + C ∫(au)du = [(au)/(lna)] + C

o ∫(lnu)du = ulnu – u + C ∫(logau)du = ∫[(lnu)/(lna)]du = [(ulnu – u)/(lna)] + C